All that identical voltages and currents aside, you don't have identical local feedback.
The feedback for both is almost entirely coming from the viewpoint of one side only.
When a one sided error occurs, you don't get the same response above and below.
And impedance is all about the feedback...
But we can fix this by attenuating the cathode's sensitivity to match the plate.
The feeling of, and response to, an upset upon either end can be evenly split.
Half properly going to the feeling end, and half copied to the unfeeling end.
Fact we can improve the balance of misbehaviors kinda proves the impedance
weren't equal to begin with.
The feedback for both is almost entirely coming from the viewpoint of one side only.
When a one sided error occurs, you don't get the same response above and below.
And impedance is all about the feedback...
But we can fix this by attenuating the cathode's sensitivity to match the plate.
The feeling of, and response to, an upset upon either end can be evenly split.
Half properly going to the feeling end, and half copied to the unfeeling end.
Fact we can improve the balance of misbehaviors kinda proves the impedance
weren't equal to begin with.
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i am not looking to get impressed, i just wanted to see the fruit of your "theory tree" to find out how it is different from other designs i have seen before....
Tony, I can refer you to Mu Followers. I can also refer you to a re-working of the cascade feedback pair used as a line stage in the Dynaco Pas 3. This was published a number of years back in The Audio Amateur.
One of the issues with that line stage involved the pole pair inserted by the two coupling caps in the global loop. Aggravated by the large amount of feedback employed to reduce the closed loop gain, the result was a big infrasonic peak in the response right around the record warp frequency.
The solution I crafted was to add an additional coupling cap in series with the input and connect the junction of the two caps through a resistor to the input stage cathode. This formed a second order high pass filter which was tuned so that the response was flat over the audio band and there was no longer any infrasonic peak.
I suppose I could reconstruct the circuit and its values if you're interested. Probably easier than leafing through all of my TAA's to find the article. I could also derive the properties of the Mu Follower if you’re interested.
You might also be interested in http://www.edn.com/design/analog/4363970/Design-second-and-third-order-Sallen-Key-filters-with-one-op-amp .
Phew! Feels like an interview. Hope I get the job!
If not, at least the secret handshake.
One of the issues with that line stage involved the pole pair inserted by the two coupling caps in the global loop. Aggravated by the large amount of feedback employed to reduce the closed loop gain, the result was a big infrasonic peak in the response right around the record warp frequency.
The solution I crafted was to add an additional coupling cap in series with the input and connect the junction of the two caps through a resistor to the input stage cathode. This formed a second order high pass filter which was tuned so that the response was flat over the audio band and there was no longer any infrasonic peak.
I suppose I could reconstruct the circuit and its values if you're interested. Probably easier than leafing through all of my TAA's to find the article. I could also derive the properties of the Mu Follower if you’re interested.
You might also be interested in http://www.edn.com/design/analog/4363970/Design-second-and-third-order-Sallen-Key-filters-with-one-op-amp .
Phew! Feels like an interview. Hope I get the job!
If not, at least the secret handshake.
don't get me wrong, i am more interested in topology rather than an actual circuit......i'd be more interested in your tube amp topologies......the circuit you linked has been discussed here many time over in the past....
re: mu-followers,....i read Allan Kimmel's article and is quite familiar with it although i have to admit that i have yet to build it.....right now my preference tube amps is for simple circuits with minimal coupling caps in the signal path......
i hate long discourses so if i were interviewing you for a job, i'd give you a hard time, but you still get the job....
Kimmel's article dealt with what he termed the Mu Stage, a pentode version of the triode Mu Follower. The article was preceded by the disclosure of the Mu Follower in letters to the editor in TAA 2/85, p.51 and 3/91, p.43. The letters gave equations describing the gain, Zout and PSRR of the MF and discussed the low distortion benefit of virtual current source loading of the bottom triode. If memory serves, the treatment in the article was not as comprehensive.
But preceding the letters were U.S. patents 2,310,342 (1943) and 2,631,197 (1953) (found thanks to John Broskie's archives and memory) which presented the topology and discussed some but not all of the above advantages.
Could you kindly steer me to discussions of the circuit I had linked to? Thanks in advance.
But preceding the letters were U.S. patents 2,310,342 (1943) and 2,631,197 (1953) (found thanks to John Broskie's archives and memory) which presented the topology and discussed some but not all of the above advantages.
Could you kindly steer me to discussions of the circuit I had linked to? Thanks in advance.
I built the Cdyne shown below.
I wanted to determine the impedance Zpk between the plate and cathode (points P and K). I started by measuring the AC voltages Vp at P (171.8mV) and Vk at K (172.2mV). Sure enough, they were for all practical purposes equal and opposite. I then shorted P’ to K’ and found that these voltages fell equally by 3dB (to 120.8 and 121.2mV) at 588Hz. At that frequency, the reactance of the capacitors in series, 164 ohms, is about what we’d expect from this triode for a value of 2/gm – the impedance between the plate and cathode.
While I had P’ shorted to K’, I decided to measure the voltage Vp’k’ at that point. It was an insignificant 3.5mV. (I expect the non-zero value was mostly due to a slight mismatch between the caps.) I decided to ground P’ and K’ to replicate the circuit SY claims can be used to determine Zpg and Zkg, the plate and cathode impedances to ground. But I checked Vp and Vk again and got virtually the same values, 117.4 and 122.4mV. The voltages were still opposite and equal, so practically all of the current out of the cathode through Ck had to go back through Cp into the plate. Therefore only a negligible amount found its way into ground.
So in grounding P’ and K’, there were no significant changes in any voltages or currents in the circuit, no changes in the parameters being measured to calculate impedance and no changes in the test methodology. With no significant changes of any kind, we can’t possibly be changing the parameter we’re testing from Zpk to Zpg and Zkg. Clearly, we’re still just testing Zpk, because nothing that we were doing - or measuring - changed.
Now, are there any models of a balanced Cdyne which correctly predict the unshorted voltages Vp and Vk and the impedance Zpk?
Yes. There is an infinity of them. They look like this:
What can we infer from our experimental data for the value of R? Absolutely nothing! Vc is virtually zero, so R? can be zero (per SY) or infinity (per Burkhart Vogel.) In neither case will it draw any current. It has no effect on circuit performance since Vp = -Vk, Vc = 0, and there is never a voltage across R?, so no current flows through it whatever its value.
The point is that the empirical data obtained from testing a balanced Cdyne cannot possibly determine the value of R?, so it certainly cannot establish the value of Zpg or Zkg, which R? must strongly influence.
It has been suggested that if the circuit were modified by adding identical capacitors across Rk and Rp and applying a square wave to the grid, the equal and opposite voltages and the time constant of the response would establish that Zpg and Zkg were both 1/gm. But the data from this experiment has the same problem with respect to R? indeterminacy as the previous one did. Any value of R? will work, so Zpg and Zkg cannot be determined.
There has not yet been a single experiment with a balanced Cathodyne put forth that can determine the value of R? even approximately. And without a known value of R?, Zpg and Zkg cannot be determined. Yet there is a large and established body of work and measurements that proves that Zpg = Rp || rp + (1+μ)Rk and Zkg = Rk || (rp + Rp)/ (1+μ).
It is long past the time to stop claiming that Zpg = Zkg = 1/gm in a balanced Cathodyne.
I wanted to determine the impedance Zpk between the plate and cathode (points P and K). I started by measuring the AC voltages Vp at P (171.8mV) and Vk at K (172.2mV). Sure enough, they were for all practical purposes equal and opposite. I then shorted P’ to K’ and found that these voltages fell equally by 3dB (to 120.8 and 121.2mV) at 588Hz. At that frequency, the reactance of the capacitors in series, 164 ohms, is about what we’d expect from this triode for a value of 2/gm – the impedance between the plate and cathode.
While I had P’ shorted to K’, I decided to measure the voltage Vp’k’ at that point. It was an insignificant 3.5mV. (I expect the non-zero value was mostly due to a slight mismatch between the caps.) I decided to ground P’ and K’ to replicate the circuit SY claims can be used to determine Zpg and Zkg, the plate and cathode impedances to ground. But I checked Vp and Vk again and got virtually the same values, 117.4 and 122.4mV. The voltages were still opposite and equal, so practically all of the current out of the cathode through Ck had to go back through Cp into the plate. Therefore only a negligible amount found its way into ground.
So in grounding P’ and K’, there were no significant changes in any voltages or currents in the circuit, no changes in the parameters being measured to calculate impedance and no changes in the test methodology. With no significant changes of any kind, we can’t possibly be changing the parameter we’re testing from Zpk to Zpg and Zkg. Clearly, we’re still just testing Zpk, because nothing that we were doing - or measuring - changed.
Now, are there any models of a balanced Cdyne which correctly predict the unshorted voltages Vp and Vk and the impedance Zpk?
Yes. There is an infinity of them. They look like this:
What can we infer from our experimental data for the value of R? Absolutely nothing! Vc is virtually zero, so R? can be zero (per SY) or infinity (per Burkhart Vogel.) In neither case will it draw any current. It has no effect on circuit performance since Vp = -Vk, Vc = 0, and there is never a voltage across R?, so no current flows through it whatever its value.
The point is that the empirical data obtained from testing a balanced Cdyne cannot possibly determine the value of R?, so it certainly cannot establish the value of Zpg or Zkg, which R? must strongly influence.
It has been suggested that if the circuit were modified by adding identical capacitors across Rk and Rp and applying a square wave to the grid, the equal and opposite voltages and the time constant of the response would establish that Zpg and Zkg were both 1/gm. But the data from this experiment has the same problem with respect to R? indeterminacy as the previous one did. Any value of R? will work, so Zpg and Zkg cannot be determined.
There has not yet been a single experiment with a balanced Cathodyne put forth that can determine the value of R? even approximately. And without a known value of R?, Zpg and Zkg cannot be determined. Yet there is a large and established body of work and measurements that proves that Zpg = Rp || rp + (1+μ)Rk and Zkg = Rk || (rp + Rp)/ (1+μ).
It is long past the time to stop claiming that Zpg = Zkg = 1/gm in a balanced Cathodyne.
Except for your data, which agree with that conclusion as long as you kept the loads equal. It's the very symmetry you deride which causes this useful behavior, the exact canceling of plate and cathode signal currents to ground. Everything you saw (and I congratulate you for actually building and measuring something!) is consistent with Figure 3 (the two Thevenin source model) in my article.
The absence of ground current is a feature, not a bug.
The absence of ground current is a feature, not a bug.
Were that I could applaud you for engaging in analysis.
Here are some of the multiple models that your and my experimental data simultaneously support:
Except for the one on the left, they are all inconsistent with your Figure 3 & 2.
You have offered no experimental verification of your conclusion that Zpg = Zkg = 1/gm. Your experimental data do not lead to the determination of R? at all. This is why BV's floating source explains balanced Cdyne operation as well as your grounded ones - because balanced Cdyne operation in no way constrains or determines the value of R? in your models.
With the high position that experimental verification occupies in your toolkit, you should be able to come up with an experiment to refute the assertion that R? is, oh, I don't know, 1537 ohms. Can you?
Here are some of the multiple models that your and my experimental data simultaneously support:
Except for the one on the left, they are all inconsistent with your Figure 3 & 2.
You have offered no experimental verification of your conclusion that Zpg = Zkg = 1/gm. Your experimental data do not lead to the determination of R? at all. This is why BV's floating source explains balanced Cdyne operation as well as your grounded ones - because balanced Cdyne operation in no way constrains or determines the value of R? in your models.
With the high position that experimental verification occupies in your toolkit, you should be able to come up with an experiment to refute the assertion that R? is, oh, I don't know, 1537 ohms. Can you?
If they give the same predictions, then they're consistent. The one on the left actually represents the way the circuit is used so is probably the best to use for those who design and build amplifiers.
So then, BV's model is wrong?
By definition, in a balanced situation, with or without capacitive loading, the voltage in the center of the model is 0V. There is no potential difference across R?; no current flows through it regardless of its value. If there were a difference, the circuit wouldn't be balanced.
Since no current flows through it, the circuit cannot possibly be measuring it. If it is not being measured, it is unknown to tests constrained by balance in the Cdyne. Since R? is clearly a part of Zkg and Zpg, they are also unknown.
If you are referring to the square wave test in your article with matched R-C loads on the P and K, the 2/gm impedance between the P and K explains things perfectly. Imagine BV's floating source of impedance 2/gm presenting a square wave. The P & K voltages are equal and opposite, and the time constant is gm/C. His model achieves this with a value of R? = ∞, as does yours with R? = 0, making my point.
There is simply no experimental evidence to support the claim that Zpg = Zkg = 1/gm.
Results are in
The global loops are now open. Operating points and input levels
normalized for same full scale output as previously given example.
I really expected unequal impedance (while driving A2) to be far
and away inferior to the equal impedance model. In practice, the
equalization of Z's made measurable but insignificant difference.
Is transformer splitter (DC crutch) invalidating the Concertina test?
True, but 7.5X more AC current does take cap coupled paths. So I
would expect some Concertina model validity to survive? I'm just
not seeing damage of the sort I surely imagined would be there...
We are driving A2 current swings to the Concertina quiescent limit.
Under these brutal non-linear load conditions, it should matter a lot.
So why here did it matter so little?
The global loops are now open. Operating points and input levels
normalized for same full scale output as previously given example.
I really expected unequal impedance (while driving A2) to be far
and away inferior to the equal impedance model. In practice, the
equalization of Z's made measurable but insignificant difference.
Is transformer splitter (DC crutch) invalidating the Concertina test?
True, but 7.5X more AC current does take cap coupled paths. So I
would expect some Concertina model validity to survive? I'm just
not seeing damage of the sort I surely imagined would be there...
We are driving A2 current swings to the Concertina quiescent limit.
Under these brutal non-linear load conditions, it should matter a lot.
So why here did it matter so little?
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